| 1 | /* -*- mode: c++; tab-width: 4; indent-tabs-mode: nil; c-basic-offset: 4 -*- */ |
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| 2 | |
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| 3 | /* |
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| 4 | Copyright (C) 2006, 2007, 2015 Ferdinando Ametrano |
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| 5 | Copyright (C) 2006 Cristina Duminuco |
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| 6 | Copyright (C) 2007 Giorgio Facchinetti |
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| 7 | Copyright (C) 2015 Paolo Mazzocchi |
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| 8 | |
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| 9 | This file is part of QuantLib, a free-software/open-source library |
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| 10 | for financial quantitative analysts and developers - http://quantlib.org/ |
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| 11 | |
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| 12 | QuantLib is free software: you can redistribute it and/or modify it |
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| 13 | under the terms of the QuantLib license. You should have received a |
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| 14 | copy of the license along with this program; if not, please email |
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| 15 | <quantlib-dev@lists.sf.net>. The license is also available online at |
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| 16 | <http://quantlib.org/license.shtml>. |
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| 17 | |
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| 18 | This program is distributed in the hope that it will be useful, but WITHOUT |
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| 19 | ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS |
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| 20 | FOR A PARTICULAR PURPOSE. See the license for more details. |
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| 21 | */ |
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| 22 | |
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| 23 | #ifndef quantlib_abcd_math_function_hpp |
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| 24 | #define quantlib_abcd_math_function_hpp |
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| 25 | |
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| 26 | #include <ql/types.hpp> |
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| 27 | #include <ql/errors.hpp> |
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| 28 | #include <vector> |
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| 29 | |
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| 30 | namespace QuantLib { |
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| 31 | |
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| 32 | //! %Abcd functional form |
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| 33 | /*! \f[ f(t) = [ a + b*t ] e^{-c*t} + d \f] |
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| 34 | following Rebonato's notation. */ |
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| 35 | class AbcdMathFunction { |
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| 36 | |
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| 37 | public: |
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| 38 | /*! \deprecated Use `auto` or `decltype` instead. |
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| 39 | Deprecated in version 1.29. |
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| 40 | */ |
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| 41 | QL_DEPRECATED |
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| 42 | typedef Time argument_type; |
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| 43 | |
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| 44 | /*! \deprecated Use `auto` or `decltype` instead. |
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| 45 | Deprecated in version 1.29. |
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| 46 | */ |
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| 47 | QL_DEPRECATED |
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| 48 | typedef Real result_type; |
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| 49 | |
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| 50 | AbcdMathFunction(Real a = 0.002, |
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| 51 | Real b = 0.001, |
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| 52 | Real c = 0.16, |
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| 53 | Real d = 0.0005); |
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| 54 | AbcdMathFunction(std::vector<Real> abcd); |
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| 55 | |
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| 56 | //! function value at time t: \f[ f(t) \f] |
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| 57 | Real operator()(Time t) const; |
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| 58 | |
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| 59 | //! time at which the function reaches maximum (if any) |
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| 60 | Time maximumLocation() const; |
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| 61 | |
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| 62 | //! maximum value of the function |
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| 63 | Real maximumValue() const; |
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| 64 | |
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| 65 | //! function value at time +inf: \f[ f(\inf) \f] |
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| 66 | Real longTermValue() const { return d_; } |
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| 67 | |
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| 68 | /*! first derivative of the function at time t |
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| 69 | \f[ f'(t) = [ (b-c*a) + (-c*b)*t) ] e^{-c*t} \f] */ |
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| 70 | Real derivative(Time t) const; |
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| 71 | |
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| 72 | /*! indefinite integral of the function at time t |
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| 73 | \f[ \int f(t)dt = [ (-a/c-b/c^2) + (-b/c)*t ] e^{-c*t} + d*t \f] */ |
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| 74 | Real primitive(Time t) const; |
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| 75 | |
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| 76 | /*! definite integral of the function between t1 and t2 |
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| 77 | \f[ \int_{t1}^{t2} f(t)dt \f] */ |
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| 78 | Real definiteIntegral(Time t1, Time t2) const; |
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| 79 | |
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| 80 | /*! Inspectors */ |
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| 81 | Real a() const { return a_; } |
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| 82 | Real b() const { return b_; } |
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| 83 | Real c() const { return c_; } |
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| 84 | Real d() const { return d_; } |
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| 85 | const std::vector<Real>& coefficients() { return abcd_; } |
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| 86 | const std::vector<Real>& derivativeCoefficients() { return dabcd_; } |
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| 87 | // the primitive is not abcd |
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| 88 | |
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| 89 | /*! coefficients of a AbcdMathFunction defined as definite |
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| 90 | integral on a rolling window of length tau, with tau = t2-t */ |
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| 91 | std::vector<Real> definiteIntegralCoefficients(Time t, |
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| 92 | Time t2) const; |
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| 93 | |
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| 94 | /*! coefficients of a AbcdMathFunction defined as definite |
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| 95 | derivative on a rolling window of length tau, with tau = t2-t */ |
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| 96 | std::vector<Real> definiteDerivativeCoefficients(Time t, |
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| 97 | Time t2) const; |
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| 98 | |
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| 99 | static void validate(Real a, |
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| 100 | Real b, |
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| 101 | Real c, |
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| 102 | Real d); |
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| 103 | protected: |
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| 104 | Real a_, b_, c_, d_; |
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| 105 | private: |
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| 106 | void initialize_(); |
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| 107 | std::vector<Real> abcd_; |
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| 108 | std::vector<Real> dabcd_; |
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| 109 | Real da_, db_; |
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| 110 | Real pa_, pb_, K_; |
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| 111 | |
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| 112 | Real dibc_, diacplusbcc_; |
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| 113 | }; |
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| 114 | |
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| 115 | // inline AbcdMathFunction |
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| 116 | inline Real AbcdMathFunction::operator()(Time t) const { |
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| 117 | //return (a_ + b_*t)*std::exp(-c_*t) + d_; |
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| 118 | return t<0 ? 0.0 : Real((a_ + b_*t)*std::exp(x: -c_*t) + d_); |
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| 119 | } |
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| 120 | |
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| 121 | inline Real AbcdMathFunction::derivative(Time t) const { |
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| 122 | //return (da_ + db_*t)*std::exp(-c_*t); |
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| 123 | return t<0 ? 0.0 : Real((da_ + db_*t)*std::exp(x: -c_*t)); |
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| 124 | } |
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| 125 | |
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| 126 | inline Real AbcdMathFunction::primitive(Time t) const { |
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| 127 | //return (pa_ + pb_*t)*std::exp(-c_*t) + d_*t + K_; |
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| 128 | return t<0 ? 0.0 : Real((pa_ + pb_*t)*std::exp(x: -c_*t) + d_*t + K_); |
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| 129 | } |
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| 130 | |
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| 131 | inline Real AbcdMathFunction::maximumValue() const { |
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| 132 | if (b_==0.0 || a_<=0.0) |
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| 133 | return d_; |
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| 134 | return (*this)(maximumLocation()); |
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| 135 | } |
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| 136 | |
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| 137 | } |
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| 138 | |
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| 139 | #endif |
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| 140 | |
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